As artificial intelligence (AI) is increasingly integrated into news production, calls for transparency about the use of AI have gained considerable traction. Recent studies suggest that AI disclosures can lead to a ``transparency dilemma'', where disclosure reduces readers' trust. However, little is known about how the \textit{level of detail} in AI disclosures influences trust and contributes to this dilemma within the news context. In this 3$\times$2$\times$2 mixed factorial study with 40 participants, we investigate how three levels of AI disclosures (none, one-line, detailed) across two types of news (politics and lifestyle) and two levels of AI involvement (low and high) affect news readers' trust. We measured trust using the News Media Trust questionnaire, along with two decision behaviors: source-checking and subscription decisions. Questionnaire responses and subscription rates showed a decline in trust only for detailed AI disclosures, whereas source-checking behavior increased for both one-line and detailed disclosures, with the effect being more pronounced for detailed disclosures. Insights from semi-structured interviews suggest that source-checking behavior was primarily driven by interest in the topic, followed by trust, whereas trust was the main factor influencing subscription decisions. Around two-thirds of participants expressed a preference for detailed disclosures, while most participants who preferred one-line indicated a need for detail-on-demand disclosure formats. Our findings show that not all AI disclosures lead to a transparency dilemma, but instead reflect a trade-off between readers' desire for more transparency and their trust in AI-assisted news content.